I <3 you. Thanks for science!
From what I can tell, to generalize, desynthing is an action, specifically, a non-skill "destructive" action (in the CompSci meaning of the term). If you can't perform other actions such as skills, you can't desynth. While Confused, Brainjacked, Fettered, Slept, Stunned, or Mounted, you cannot preform actions (including skills), so you cannot desynth. If you've readied up for a duty or you are crafting or you are in a shop window, you cannot perform unrelated "destructive" actions, so you cannot desynth. "Destructive" actions are things that permanently modify the game state such that they interfere with the action you are currently preforming. You can't switch classes while accessing a retainer's inventory as that changes your gamestate in ways that have nothing to do with accessing your retainer's inventory, but you can sort items, discard them, and move them around. You cannot move items around or discard them while crafting, because that affects your gamestate in a way that directly impacts the craft - what if you discard an item that you're currently using in a synth? You can't shop or access your retainers while crafting for the same reason.
The big difference between crafting/gathering/shopping/retainering and desynthing is that desynthing does not require you to stand still, nor be in a specific place, nor interact with a specific non-inventory object. So, you can do it on the go, where you can't do the others on the go. There is also no class requirement for desynthing, so you can do it in duties. You can't craft in duties, not because it's disabled during duties, but because you cannot be a DoH class in a duty.
.... and now I'm wondering about crafting during Frontlines... I never checked if the DoH classes were available or not (my guess is that they aren't, or else I'd have seen trolls running out brandishing their sewing needles already).